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Recap of the last 12 lectures

Polymers and Polymerization Techniques

Batch and Continuous Processes

Synthesis and Production of:

TTL212: Manufactured Fibre Technology

Nylon 6

Nylon 66

PET

PAN

Modification of PET and Nylons

Outline of Next Few Lectures

Fundamental of Spinning

Introduction to spinning and thermodynamics ofspinning.

Polymer rheology including shear flow through acapillary and elongational flow in a Spinning

line.

Melt instabilities. Momentum and heat transport in spinning.

Introduction

1) Acquisition of spinnable liquid Polymer melt or solution

2) Jet formation:

Under pressure through capillaries

. .

Length: Equal to or 3-4 times dia

3) Jet hardening Pulled on winder

Attenuated and solidified

Uniform cross section

Fibre Spinning Methods

Melt spinning

Dry spinning

Wet spinning

Melt spinning Dry spinning Wet spinning

Nylon 6,6

Nylon 6

PET

PE

PP

Cellulose

diacetate

Cellulose

triacetate

Acrylic

Polyurethane Polyvinyl

chloride

Chlorinated PVC

Acrylic

Modacrylic

Rayon

Polyurethane

Polyvinyl

alcohol Aromatic

polyamide

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Melt Spinning

Simplest, youngest and most economical

Melt stable material

Solidification requires only heat transfer

Fast production rates

Smooth and circular fibres

Polymers can be blended with plasticizers

for stable melt

Melt Spinning Set-Up

Solution Spinning

Dry Spinning

Solidification achieved by solvent

evaporation

Solidification requires one way mass

transfer

Wet Spinning

Solidification by chemical coagulation

Solidification requires two way mass

transfer

Dry Spinning

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Wet Spinning Special Techniques

Dry jet wet spinning: aromatic polyamides

Gel spinning: Ultra high molecular weight

PE

Electrospinning: for producing nanofibres

Thermodynamics of Spinning

Low molecular weight compounds: continuous

change of neighbours

Polymeric compounds: Rotatory segmental

jumps

Quiescent state:

Number of jumps in 1 direction = Number of

jumps in other direction

So, no net transport: self diffusion

External stress: Preferential movement in

direction of stress (flow)

Ease of this depends on viscosity

For flow to become possible: activation energyneeded

With increase in C atoms, activation energy:

1. first increases

2. rate of increase becomes slower

3. becomes constant (25 carbon atoms)

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Thermodynamics of Spinning

Low molecular weight compounds: continuous

change of neighbours

Polymeric compounds: Rotatory segmental

jumps

Quiescent state:

Number of jumps in 1 direction = Number of

jumps in other direction

So, no net transport: self diffusion

External stress: Preferential movement in

direction of stress (flow)

Ease of this depends on viscosity

For flow to become possible: activation energyneeded

With increase in C atoms, activation energy:1. first increases

2. rate of increase becomes slower

3. becomes constant (25 carbon atoms)

States of Polymer Liquid

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Todays Lecture

Polymer Rheology

- ew on an u s

What is rheology??

The study of deformation and flow.

What is rheology? What is Rheology?An answer for your baffled family and friends. *

Rheology is the study of the flow of materials that behave in an

interesting or unusual manner. Oil and water flow in familiar, normal

ways, whereas mayonnaise, peanut butter, chocolate, bread dough,

and silly putty flow in complex and unusual ways. In rheology, we

study the flows of unusual materials.

all normal or Newtonian fluids (air, water, oil, honey) follow the

same scientific laws. On the other hand, there are also fluids that do

not follow the Newtonian flow laws. These non-Newtonian fluids, for

example mayo, paint, molten plastics, foams, clays, and many other

fluids, behave in a wide variety of ways. The science of studying

these types of unusual materials is called rheology

*Faith Morrison, The News and Information Publication of The Society of Rheology, Vol 73(1) Jan 2004, pp 8-10

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Rheology Core: Viscosity and Elasticity Examples of Complex Fluids Foods

Emulsions (mayonaisse, ice cream)

Foams (ice cream, whipped cream)

Suspensions (mustard, chocolate)

Gels (cheese)

Biofluids Suspension (blood)

Gel (mucin)

Solutions (spittle)

Personal Care Products Suspensions (nail polish, face scrubs)

Solutions/Gels (shampoos, conditioners)

Foams (shaving cream)

Electronic and Optical Materials Liquid Crystals (Monitor displays)

Melts (soldering paste)

Pharmaceuticals Gels (creams, particle precursors)

Emulsions (creams)

Aerosols (nasal sprays)

Polymers

Rheologys Goals

1. Establishing the relationship between applied

forces and geometrical effects induced by

these forces at a point (in a fluid).

e ma ema ca orm o s re a ons p s ca e

the rheological equation of state, orthe

constitutive equation.

The constitutive equations are used to solve

macroscopic problems related to continuum

mechanics of these materials. Any equation is just a model of physical reality.

Rheologys Goals

1. Establishing the relationship betweenrheological properties of material and itsmolecular structure (composition).

Related to: s ma ng qua y o ma er a s

Understanding laws of molecular movements

Intermolecular interactions

Interested in what happens inside a point duringdeformation of the medium.

What happens inside a point?

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Rheological Behaviour of Fluids: NewtonianNEWTONIAN FLUIDS

Newtonian: Plot of rate of shear againstshear stress is a straight line passing throughthe origin provided flow is laminar

Examples:

1.Water

2.Simple Organic Liquids

3.True Solutions

4.Dilute suspensions

5.Emulsions

6.Gases

Laminar flow, sometimes known as streamline flow, occurswhen a fluid flows in parallel layers, with no disruption

between the layers. At low velocit ies the fluid tends to flow

without lateral mixing, and adjacent layers slide past one

another like playing cards. There are no cross currents

perpendicular to the direction of flow, nor eddies or swirls of

fluids. In laminar flow the motion of the particles of fluid is

very orderly with all particles moving in straight lines parallel

to the pipe walls

Incompressible fluid is a fluid which is not reduced involume by an increase in pressure.

Viscous Flow and Newtonian Fluids

Force F (dyn) applied on upper plane

Shear stress (F/A dyn cm )

Moves with velocity relative to lower plane

Streamline or laminar flow: material planes sliding

over another

An le measure of shear strain

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Rate of shear = /dt

Velocity along C = u

Velocity along D = u + (du/dy)

Then, in time t,

Distance moved by P = u t

Distance moved by Q = [u + (du/dy) ] t

Now,

So, in the limit,

= u y

i.e. rate of shear of liquid is equal to the

velocity gradient normal to the direction of

the flow

Newton observed:

For laminar flow, shear stress acting over

surfaces parallel to the direction of flow

needed to maintain a given shear rate is

proportional to the shear rate.

Thus,

d/dt

or

= d/dt

Where

= coefficient of viscosity

is constant for

Given liquid

Given temperature

Given pressure

CGS system: dyn s cm

Note: If a force of 1 dyn acting on 1 cm area results in a shear rat of 1 s, thenviscosity is 1 dyn s cm or 0.1 Pas or 1poise.

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CAPILLARY FLOW

Flow through capillary derived by

Poiseuille

Flow is assumed to be

. ream ne am nar

2. Pressure constant over any cross

section

3. No radial flow

Adjacent layers: different speeds

Incompressible, Newtonian liquid of

Density , Viscosity

Ca illar of radius R and len th L

Let velocity of layer at distance r from the axis be V

is the shear stress

If P is applied pressure (pressure difference between inlet

and outlet),

accelerating force acting on liquid cylinder of radius r,

Fpressure = Pr

Viscous drag, Fviscosity = X 2rL

When the conditions are steady, these two

forces must be equal and opposite,

Pr = - X 2rL

= - (dV/dr) X 2rL

or

-

At the wall of tube, r = R and velocity = 0

Integrating,

R - r = 4LV/Por V = P(R - r)/4L

The profile of the advancing liquid is

therefore a parabola.

Fluid flow through a capillary (a) laminar flow (b) parabolic velocity

profile

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The volume of the liquid dQ flowing through

the tube of thickness dr per second is

dQ = 2 rVdr

Hence, the total volume of the liquid flowing

through the tube per second, is

This may be rearranged as

= PR/8QL

This is called Poiseuilles equation

Two assumptions:

Liquid is Newtonian

All the energy supplied to push the liquid

through the capillary is used to overcome

the viscous drag or internal friction or

rheological force.

CAPILLARY FLOW

Flow through capillary derived by

Poiseuille

Flow is assumed to be

1. Streamline/Laminar

2. Pressure constant over any cross

section

3. No radial flow Adjacent layers: different speeds

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Incompressible, Newtonian liquid of

Density , Viscosity

Ca illar of radius R and len th L

Let velocity of layer at distance r from the axis be V

is the shear stress

If P is applied pressure (pressure difference between inlet

and outlet),

accelerating force acting on liquid cylinder of radius r,

Fpressure = Pr

Viscous drag, Fviscosity = X 2rL

When the conditions are steady, these two

forces must be equal and opposite,

Pr = - X 2rL

= - (dV/dr) X 2rL

or

-

At the wall of tube, r = R and velocity = 0

Integrating,

R - r = 4LV/Por V = P(R - r)/4L

The profile of the advancing liquid is

therefore a parabola.

Fluid flow through a capillary (a) laminar flow (b) parabolic velocity

profile

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The volume of the liquid dQ flowing through

the tube of thickness dr per second is

dQ = 2 rVdr

Hence, the total volume of the liquid flowing

through the tube per second, is

This may be rearranged as

= PR/8QL

This is called Poiseuilles equation

Two assumptions:

Liquid is Newtonian

All the energy supplied to push the liquid

through the capillary is used to overcome

the viscous drag or internal friction or

rheological force.

NEWTONIAN FLUIDS

Newtonian: Plot of rate of shear againstshear stress is a straight line passing throughthe origin provided flow is laminar

Examples:

1.Water

2.Simple Organic Liquids

3.True Solutions

4.Dilute suspensions

5.Emulsions

6.Gases

NON NEWTONIAN FLUIDS

Do not exhibit the characteristics of Newtonian

Polymer melts and solutions

Fluids in general can be divided into 2 categories:

a) Time independent : rate of shear is a function ofshearing stress

b) Time dependent: Shear stress-shear raterelationships depend on how fluid has beensheared and its history

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TIME INDEPENDENT FLUIDSLine A: Newtonian fluid

Line B: Bingham body

Line C: Shear thinning/pseudoplastic

Line D: Shear thickening/dilatant

Bingham body: Connected internal structurethat collapses above a yield stress

Above yield stress (y ), shear rate increases

linearly with shear stress i.e.

= ( y ) where y.

Examples: Pottery clay, chocolate,

toothpaste, butter

Pseudoplastic flow: Apparent viscosity

decreases as the rate of shear is increased

Slope of OP

> OP

=> <

Examples: polymer melts and solutions,

natural resins, rubbers, bitumens, heavy

oils

Advantage:Reduction in viscosity with increasing rate of shear

Stresses required to produce high flow rates not as highas expected from viscosity measurements at low shear

rates

This reduces power requirements for processing toa considerable extent

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Cause of shear thinning

Extensively entangled and randomly

oriented nature of long chain molecules

Shear rate increases, molecules become

aligned so points of entanglements reduced

Loss of existing entanglements higher than

rate of generating new ones

Number of entanglements in a given volume

has lower e uilibrium values at lar er shear

rates

Frictional resistance between adjacent layer

of the laminar fluid decreases

Very high shear rates orientation of molecules complete, near Newtonian

behaviour

Dilatant fluids: Increase in apparent viscosity with

increase in shear rate

Highly concentrated suspensions, particularly PVC

pastes

Irregularly shaped particles, closely packed with

minimum voids in the stress free rate

ow s ear ra e: o par c es o no ma e muc

contact

High shear rate: Particles do not pack easily, rubbing

friction enhances resistance to flow

Sand water suspensions, clay suspensions, printing inks Power law equation (n>1):

= k()n.

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TIME DEPENDENT FLUIDS

Thixotropic: At a constant shear stress orshear rate, the viscosity falls as time increases

Time dependent collapse of ordered structurewhich breaks down to a lower apparentviscosity when sheared.

Reversible effects.

Paints, shaving cream, margarine, printing ink.

Rheopectic:Apparent viscosity increases withtime.

Thixotropic

Rheopectic